The correct option is
B Theirs
When a pronoun in possessive case is placed before the noun being described it is called a possessive adjective. Example: This is their book. In this sentence, the word, 'their' is a possessive adjective.Sometimes, the pronoun in possessive case is used alone (and not before the noun). In such case, it is called a possessive pronoun Example: This book is theirs. Here, the word, 'theirs' is a possessive pronoun.
In the given sentence, the noun being described is Sabah and Sarah's house. It may be noted that the house belongs to both Sabah and Sarah. Hence, the pronoun which can fill the blank space should be plural.
Among the given options, the words, 'his' and 'her' are singular possessive adjectives. Hence, options A and B are incorrect.
We also observe that the pronoun is used alone i.e it is not placed before the noun- house. In fact, the noun (house) is omitted in the second sentence and is implied. Hence, we have to choose a possessive pronoun and not a possessive adjective.
The word, 'their' is a possessive adjective i.e it is usually placed before the noun. Example: This is their house. It cannot be used alone. Hence, option C is incorrect.
Option D is correct as the word, 'theirs' is a possessive pronoun which can be used alone.